Seven of the designated individuals are current or former senior Venezuelan officials and one was otherwise identified by the United States as undermining democracy in the country.
The assembly's first action was to fire Venezuela's chief prosecutor, who had accused Maduro of human rights abuses, confirming opposition fears that the assembly would purge the government of dissenting voices.
The US Treasury website notes that Frias Chavez is a member of Venezuela's Constituent Assembly and Secretary of Venezuela's Presidential Commission for the Constituent Assembly.
In theory, both the National Assembly and the pro-government constitutional assembly can rule simultaneously, but the new super body created through a July 30 election that drew global condemnation has the authority to trump any other branch of government-and Venezuela's leaders have promised to do just that. That means opposition groups are prohibited from acting in a way that interferes with laws it passes.
Former Foreign Minister Delcy Rodriguez, who is leading the assembly but has so far escaped being sanctioned, said the latest US action seeks to "spread fear" among delegates and please government opponents she described as "criminals" and "unpatriotic".
The president called the vote for a constitutional assembly to overhaul Venezuela's political system in May after a month of protests against his government, which has overseen the country's descent into a devastating crisis during its four years in power.
All sanctioned individuals have had all their US assets frozen, and Americans are barred from doing business with them.
Maduro and his allies have consistently blamed the opposition for political violence that has erupted at protests and left more than 120 Venezuelans dead.
The installation of the Assembly will likely intensify the country's political crisis as Maduro's socialist government has faced growing worldwide criticism in recent weeks.
President Nicolas Maduro's all-powerful constitutional assembly is forging ahead on promises to punish the embattled leader's foes.More news: The ACLU just filed a lawsuit defending Milo Yiannopoulos
The U.S. Treasury announced the sanctions were against those involved in organizing or supporting the country's new constituent assembly, which granted President Nicolas Maduro virtually unlimited powers.
This would seem to indicate that there may be some new legislative elections in the future, serving as a fig leaf to give the appearance of representative government, but those offices will have no power.
On Tuesday, the United Nations joined the growing criticism of the government, saying Venezuela had used excessive force to crush anti-government protests.
The opposition-led National Assembly "will be a body that in principal co-exists with the constitutional assembly but that will surely be displaced in practice", Magdaleno said.
One of them is Adan Chavez Frias, older brother of the late Hugo Chavez and minister of Culture until his election to the Constituent Assembly.
The fading out of democratic institutions in recent times has reached its culmination and what we have in Venezuela is a dictatorship, Luna said.
Russia, however, said the vote was laying the basis for a peaceful resolution of the issues plaguing Venezuelan society.
Rodriguez stepped down as Venezuela's foreign minister in June.
For all of Maduro's anti-capitalist rhetoric, Venezuela, which sits atop the world's largest oil reserves, remains highly dependent on oil exports to the USA, especially for importing food and medicine - items in short supply as crude prices have fallen and triple-digit inflation wreaks havoc on the economy.